Author:  Su, Zhongdi 
Title:  Numerical studies of fluidstructure interaction for cylinder array in various configurations 
Degree:  Ph.D. 
Year:  2004 
Subject:  Hong Kong Polytechnic University  Dissertations Fluidstructure interaction Cylinders  Fluid dynamics 
Department:  Dept. of Mechanical Engineering 
Pages:  242 leaves : ill. ; 30 cm 
Language:  English 
InnoPac Record:  http://library.polyu.edu.hk/record=b1762030 
URI:  http://theses.lib.polyu.edu.hk/handle/200/173 
Abstract:  This thesis presents numerical studies of fluidstructure interaction for cylinder arrays in various configurations in cross flow. The primary objective of the studies is to acquire, through numerical simulations, an improved understanding of fluidstructure interaction of two circular cylinders in cross flow. Three numerical methods including finite element method (FEM), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM) are applied in this thesis. Some of the numerical results have been validated by experimental visualization using Laser Induced Fluorescence (LIF) method. Six topics are involved in this thesis. Firstly, laminar flow over two cylinders in tandem has been experimentally and numerically studied. The Reynolds numbers under consideration are 200 and 1000 and the spacing ratios are 2.0, 3.0, 4.0 and 5.0. The computation is mainly carried out by the 2D finite element method. The Laser Induced Fluorescence experiments are carried out to verify the calculated results. 3D lattice Boltzmann method is also employed in the cases of Re200. In the case of Re=200, both the 2D and 3D calculations are quite consistent with the experimental visualization. Both the 2D and 3D calculations and experimental visualization indicate that the critical spacing ratio is between 4.0 and 5.0. In the case of Re=1000, the 2D calculations are also consistent with the experimental visualization. However, the critical L/D is reduced to between 3.0 and 4.0 due to the instability of high momentum shear layer. Secondly, a numerical study of a twotandem cylinders system in turbulent flow has been attempted using a standard ke turbulence model plus a modified wall function. The numerical method is 2D finite element method (FEM). Different L/D from 1.5 to 10 are selected to consider the effect of spacing ratio. At a special spacing ratio, LID=3.5, the calculations are carried out at Re=10(4)10(5) to investigate the effect of Re on the wake structure. At L/D=3.5 and Re=20000, the vibration of elastic cylinder is also simulated to investigate the influence of fluidstructure interaction on separation behavior of shear layers or vortices. Calculated vortices, force time histories and Strouhal number are analyzed to understand the complicated flaw phenomena. Present numerical simulations reveal several important features, such as bistable flow, critical flow regime, effect of elasticity, lift and drag coefficients and vortex shedding frequency. Computed Strouhal numbers agree well with the previous experimental results. Good agreement in mean drag coefficients of both cylinders has been also obtained between measurements and calculations for different L/D. Thirdly, two sidebyside cylinders in a cross flow at subcritical Re over a range of T/D ratios have been numerically investigated. The Re range of this study is Re = 8,000 160,000. The four T/D ratios, T/D=1.125, 1.5, 2.0 and 3.0, are chosen because the resulting flow regimes are representative of three different proximity effects observed in two sidebyside cylinders. The mean drag, mean lift, and Strouhal number deduced from the calculated results are quite consistent with measurements. The current numerical technique could reproduce almost the same fluid dynamic characteristics in the Re range of 8000160000, such as the mean drag, mean lift, and Strouhal number. At small spacing ratio, the discrepancy between the calculation and the measurement is large. The reason may be that the current calculation is twodimensional and the wake interaction is a typically threedimensional phenomenon. Fourthly, two sidebyside cylinders with a small control cylinder at the middle symmetric line are studied both experimentally and numerically. The spacing ratios of the two sidebyside cylinders are selected to 1.5 and 2.0, which is within the range of the biased flow. The Reynolds number under consideration is 200. The calculated flow pattern is quite consistent with the experimental visualization. The calculated lift time series helps to further explain the mechanism of the wake control by the small cylinder. At intermediate spacing ratio, the small control cylinder can significantly suppress the vortex shedding from two sidebyside cylinders. When the spacing ratio is T/D=1.5, the small control cylinder can suppress the vortex shedding at downstream L/D =0~2; when the spacing ratio is T/D=2, the small control cylinder can suppress the vortex shedding at downstream L/D=1~3. This indicates that the small control cylinder make the whole system behave like an extended bluff body. With increasing the spacing ratio T/D of the two main cylinders, the small control cylinder has a wider range to suppress the wake. This study may have wider implications for the wake control of two sidebyside bluff bodies. Fifthly, the flowstructure interaction phenomenon of two staggered elastic cylinders in a cross flow is examined. The calculations are carried out at Re=200, P/D=1.5 and 庛=15o~ 75o for two rigid cylinders and two elastic cylinders. The force coefficients and cylinder displacements, and their power spectra are analyzed to help understanding the physics of fluidstructure interaction. The present results for two rigid cylinders at Re = 200 are in good agreement with experimental measurements. At Re=1000, the current results on the flow pattern are in fair agreement with experimental visualizations. Current results obviously show that the characteristics of flowinduced vibration change with 庛. In particularly, attraction (庛<=30o) and repulsion (庛>=45o) between the two cylinders are observed numerically with changing 庛. Finally, a threedimensional circular cylinder with end walls in a cross flow is numerically studied at aspect ratios of a=8,16 and 24 and Reynolds number of Re=100 and 300. We focus on the effect of end wall and aspect ratio on the vortex shedding pattern and seek deep understanding of relation between the vortex shedding patterns and aspect ratio and the variation of flow induced forces along cylinder span. Finite volume method and lattice Boltzmami method are used to carry out the calculations. The numerical results obtained from FVM and LBM at Re=100 both fit the available established measurements well. At Re=100, the vortex shedding in the cylinder wake is laminar, with constant shedding frequency but variant shedding phase angle along the cylinder span. The maximum phase angle difference is about 90o. Significant variation in the lift and drag coefficients along the cylinder span is observed at Re=300 when the end plates are presented and the aspect ratio is lower than 24. The end plates suppress the vortex shedding and delay the transition to turbulence heavily in the cylinder wake. At Re=300, the wake is actually laminar at a = 8, and threedimensional transitional at a = 16 and 24. Oblique cellular vortex shedding pattern is observed in the cylinder wake at Re=300 and a=16 and 24.This is the main reason for the frequency modulation in the time histories of lift coefficients along the cylinder span. 
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